Local solutions with infinite energy of the Maxwell-Chern-Simons-Higgs system in Lorenz gauge

TL;DR

This paper proves local well-posedness for the Maxwell-Chern-Simons-Higgs system in Lorenz gauge with low regularity data, utilizing a null condition to improve previous results.

Contribution

It introduces a null condition approach to establish local well-posedness for the system with less regular initial data, advancing the understanding of its mathematical properties.

Findings

Established local well-posedness for low regularity data

Utilized null condition to improve prior results

Enhanced mathematical understanding of the system's solutions

Abstract

We consider the Maxwell-Chern-Simons-Higgs system in Lorenz gauge and use a null condition to show local well-psoedness for low regularity data. This improves a recent result of J. Yuan.